Question

What will be the exponents of all the prime factors of $1728$? Evaluate using step diagram method.

• A. Exponent of $2$ is $6.$
• B. Exponent of $2$ is $3.$
• C. Exponent of $3$ is $3.$
• D. Exponent of $3$ is $6.$

Answer 1

Answer: (A), (C)

Exponent of $3$ is $3.$

By finding all the factors of $1728$ by step diagram method we get,


$1728=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
$\Rightarrow 1728=2^6\times 3^3$
So, exponent of prime factor $2$ is $6$ and that of $3$ is $3$.